Downing Street has insisted a former senior official does not speak for the Prime Minister after he claimed Theresa May had been “exasperated” by Justine Greening before sacking her.

Nick Timothy accused the former education secretary of “putting the brakes” on policies like free schools and standing in the way of a review which could have allowed universities to charge varying fees to increase competition.

The PM’s former chief of staff said Ms Greening was unpopular with officials and frustrated reformers.

Honour & privilege to serve in Govt since 2010. Social mobility matters to me & our country more than my ministerial career. I'll continue to do everything I can to create a country that has equality of opportunity for young people & I’ll keep working hard as MP for Putney.

She walked out of the Government on Monday after turning down Mrs May’s offer of a move to the work and pensions brief.

Writing in the Daily Telegraph, Mr Timothy, who left Number 10 after being blamed for the Tories’ lacklustre election campaign last year, said: “Greening was unpopular with officials, she frustrated reformers, and she exasperated the Prime Minister.

“Charged with making Britain ‘the world’s great meritocracy’, she put the brakes on policies that work, like free schools, and devised bureaucratic initiatives of little value.”

Ms Greening never dissented in public over Mrs May’s proposals to allow new grammars and increase sponsorship of state schools by universities, private schools and the Catholic church, but “stalled as far as she could”, Mr Timothy said.

He denied allegations that he “orchestrated” the Putney MP’s dismissal, but made no secret of his disdain for her record, accusing her of succumbing to a change-resistant educational establishment which he termed “the blob”.

No 10 refused to say whether Mrs May and Mr Timothy had spoken recently but attempted to distance the PM from the comments.

The Prime Minister’s official spokesman said: “Nick Timothy left Downing Street more than seven months ago and he doesn’t speak for the Prime Minister or for the Government.”

So wrong, this stuff re Justine Greening - she supported me in every single reform we undertook of our universities, was a terrific colleague and faultlessly loyal. https://t.co/9vvJdzGl7I

Mr Timothy’s criticisms of Ms Greening were rejected by former universities minister Jo Johnson, who worked under her at the Department for Education from 2016 to 2018.

Mr Johnson, who became a minister in the Department for Transport and minister for London in this week’s reshuffle, tweeted: “So wrong, this stuff re Justine Greening – she supported me in every single reform we undertook of our universities, was a terrific colleague and faultlessly loyal.”

Prominent anti-Brexit backbencher Anna Soubry voiced concern at the idea that Mr Timothy may still exert any influence in Downing Street, tweeting: “Disappointed & surprised the man who helped lose us our majority & was sacked from No 10 is still in charge…”

Ms Greening did not address the criticism as she spoke in the Commons for the first time since leaving the Cabinet.

She congratulated Amber Rudd on taking the women and equalities brief she had held alongside her work as education secretary.

The Home Secretary praised Ms Greening for the “enormous good work that she did in this role”.